Largest known prime partial sum of Dedekind numbers.
Equivalently partial sum of number of monotone Boolean
functions of n variables, or partial sums of number of
antichains of subsets of an n-set: 2 + 3 + 6 + 20 + 168 =
199 is prime. Curously, the first 5 such partial sums are
prime (2, 5, 11, 31, 199), and then no more primes are
known. [Post]

The smallest emirp formed from a double-digit number
followed by the product of its digits. [Loungrides]

In visualizing the patterns generated in the "gaps of
gaps" given by the prime numbers (e.g., below 199), a
curious pattern emerges. This shows the gaps between the
primes, followed by the absolute difference of those gaps,
followed by the absolute difference of those gaps, etc., and
on until all gaps are displayed in a (triangular) table of
values. Done as a programming exercise, I was amazed to
find patterns connecting common numbers in the table of
gaps. Most interesting of these is the "dripping triangles"
which reminds me of Wolfram diagrams. [Gene-Boggs]